Review Problem 7 solution - 1 2 9 3 2 5 X s s s s s = Thus...

7.Utilize the “final value theorem” to determine the final value of ( )x tgiven the conditions of problem 6. (The solution should be the same as that obtained by taking the limit of the solution in problem 6 as t goes to infinity.) The final value theorem states that ( )0lim( )limtsytsY s→∞→=where ( )Y sin our case is ( )X s. From Problem 1, ( )( )()002222525U ss x xX ss ss s++=+++++dotnosp. From superposition, like in Problem 6, ( )( )( )12X s X s X s=+where ( )( )1225U sX ss s=++and ( )()0022225s x xX ss s++=++dotnosp. From Problem 2, where the input is zero and the initial conditions are the same as those of Problem 7, ( )()222.2 31.6.22525ssX ss ss s+--== -++++. And from Problem 5, where the initial conditions are both zero and the input is like that of Problem 7,

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